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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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3 results for “semi-locally-simple-connectedness”

Semi-local simple connectedness of non-collapsing Ricci limit spacesmath.DG

Let $X$ be a non-collapsing Ricci limit space and let $x\in X$ . We show that for any $ε>0$ , there is $r>0$ such that every loop in $B_t(x)$ is contractible in $B_{(1+ε)t}(x)$ , where $t\in(0,r]$ . In particular, $X$ is semi-locally simply connected.

2019-04-15abs ↗pdf ↗

On the universal cover and the fundamental group of an

RCD^*(K,N)

-spacemath.MG

The main goal of the paper is to prove the existence of the universal cover for $RCD^*(K,N)$ -spaces. This generalizes earlier work of C. Sormani and the second named author on the existence of universal covers for Ricci limit spaces. As a result, we also obtain several structure results on the (revised) fundamental gro…

2016-05-10abs ↗pdf ↗

On fundamental groups of RCD spacesmath.MG

Study fundamental groups of RCD spaces without smoothness or curvature bounds.

problem Understanding fundamental groups of RCD spaces without additional conditions.

method Combining tools from RCD spaces, Gromov-Hausdorff convergence, and splitting theorems.

result Fundamental groups of RCD spaces are controlled by a finite number of generators and have specific properties under convergence.

fundamental groups RCD spaces Gromov-Hausdorff convergence splitting theorems semi-locally-simple-connectedness

2022-10-13abs ↗pdf ↗